Scilab Function
Last update : Dec 1997

cdfbet - cumulative distribution function Beta distribution

### Calling Sequence

  `[P,Q]=cdfbet("PQ",X,Y,A,B)`
  `[X,Y]=cdfbet("XY",A,B,P,Q)`
  `[A]=cdfbet("A",B,P,Q,X,Y)`
  `[B]=cdfbet("B",P,Q,X,Y,A)`

### Parameters

- `P,Q,X,Y,A,B`: five real vectors of the same size.
- `P,Q (Q=1-P)` : The integral from 0 to X of the beta distribution (Input range: [0, 1].)
- `Q`: 1-P
- `X,Y (Y=1-X)` : Upper limit of integration of beta density (Input range: [0,1], Search range: [0,1]) A,B : The two parameters of the beta density (input range: (0, +infinity), Search range: [1D-300,1D300] )

### Description

Calculates any one parameter of the beta distribution given values for the others (The beta density is proportional to `t^(A-1) * (1-t)^(B-1)`.

Cumulative distribution function (P) is calculated directly by code associated with the following reference.

DiDinato, A. R. and Morris, A. H. Algorithm 708: Significant Digit Computation of the Incomplete Beta Function Ratios. ACM Trans. Math. Softw. 18 (1993), 360-373.

Computation of other parameters involve a seach for a value that produces the desired value of P. The search relies on the monotinicity of P with the other parameter.

From DCDFLIB: Library of Fortran Routines for Cumulative Distribution Functions, Inverses, and Other Parameters (February, 1994) Barry W. Brown, James Lovato and Kathy Russell. The University of Texas.